Variable structure control: Difference between revisions

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{{refimprovemore citations needed|date=July 2011}}

'''Variable structure control''' ('''VSC)''') is a form of [[Classification of discontinuities|discontinuous]] [[nonlinear control]]. The method alters the [[dynamic system|dynamics]] of a [[nonlinear system]] by application of a high-frequency ''switching control''. The [[state space (controls)|state]]-[[feedback]] control law is ''not'' a [[continuous function]] of time; it ''switches'' from one smooth condition to another. So the ''structure'' of the control law ''varies'' based on the position of the state trajectory; the method switches from one smooth control law to another and possibly very fast speeds (e.g., for a [[countably infinite]] number of times in a finite time interval). VSC and associated sliding mode behaviour was first investigated in early 1950s in the Soviet Union by Emelyanov and several coresearchers.<ref name="E1967">{{Cite book|title= Variable Structure Control Systems|editor1-last=Emelyanov|editor1-first=S.V.|publisher=Nauka|___location=Moscow|year=1967|postscript= <!--None-->}}</ref>

The main mode of VSC operation is [[sliding mode control]] (SMC). The strengths of SMC include:

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* Finite-time convergence (due to discontinuous control law)

The weaknesses of SMC include:

* [[Switch#Contact bounce|Chatter]]ing due to implementation imperfections

* Over-focus on ''matched'' uncertainties (i.e., uncertainties that enter into the control channel)

However, the evolution of VSC is an active area of research.<ref name="EFF06">{{Cite book|title=Advances in Variable Structure and Sliding Mode Control|editor1-last=Edwards|editor1-first=CristopherChristopher|editor2-last=Fossas Colet|editor2-first=Enric|editor3-last=Fridman|editor3-first=Leonid|publisher=Springer-Verlag|___location=Berlin|year=2006|series=Lecture Notes in Control and Information Sciences|volume=vol 334|isbn=978-3-540-32800-1|postscript=<!--None-->}}</ref>

== See also ==

*[[Variable structure system]]

*[[Sliding mode control]]

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*[[Switching amplifier]]&nbsp;&ndash; Uses switching-mode control to drive continuous outputs

*[[Delta-sigma modulation]]&nbsp;&ndash; Another (feedback) method of encoding a continuous range of values in a signal that rapidly switches between two states (i.e., a kind of specialized sliding-mode control)

*[[Pulse -density modulation]]&nbsp;&ndash; A generalized form of delta-sigma modulation.

*[[Pulse-width modulation]]&nbsp;&ndash; Another modulation scheme that produces continuous motion through discontinuous switching.

== References ==

{{reflist|colwidth=30em}}

== Further reading ==

{{refbegin}}

*{{cite book

| author = [http://www.egr.msu.edu/~khalil/ Hasan K. Khalil]

| year = 2002

| edition = 3rd

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| ___location = Upper Saddle River, NJ}}

*{{cite book

| author = [http://www.ece.osu.edu/~utkin/ Utkin, V.I.]

| title = Sliding Modes in Control and Optimization

| publisher = Springer-Verlag

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| editor-first = Alan S.I.

| title = Variable Structure and Lyapunov Control

| series = Lecture Notes in Control and Information Sciences

| publisher = Springer-Verlag

| place = London

| year = 1994

| volume = 193

| isbn = 978-3-540-19869-7

| doi = 10.1007/BFb0033675

}}

*{{cite book

| editor1-last = Steinberger

| editor1-first = M.

| editor2-last = Horn

| editor2-first = M.

| editor3-last = Fridman

| editor3-first = L.

| title = Variable-Structure Systems and Sliding-Mode Control

| series = Studies in Systems, Decision and Control

| publisher = Springer-Verlag

| place = London

| year = 2020

| volume = 271

| isbn = 978-3-030-36620-9

| doi = 10.1007/BFb0033675

}}

{{refend}}

== References ==

{{reflist|colwidth=30em}}

{{DEFAULTSORT:Variable Structure Control}}